Linear Equation 26

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The sum of the digits of a two-digit number is 7. If the digits are reversed, the new
number is increased by 3, equals 4 times the original number. Find the original number.

Solution:

Let x be the digit at ten's place and y be the digit at unit place.

Therefore, the number is 10 x + y and the sum of the digits is x + y

On reversing the digits, the number becomes 10 y + x

According to the problem,

x + y = 7 ---------------------------------------------------- (i)

and, 10 y + x + 3 = 4 (10 x + y) ----------------------------- (ii)

on solving, we get x = 1 and y = 6

Therefore, Required number = 10 x + y = 10 X 1 + 6 = 16

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